This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
In this chapter, the emphasis is on the mechanics of equation solving, which clearly explains how to isolate a variable. The goal is to help the student feel more comfortable with solving applied problems. Ample opportunity is provided for the student to practice translating words to symbols, which is an important part of the "Five-Step Method" of solving applied problems (discussed in modules (<link document="m21980"/>) and (<link document="m21979"/>)).
Objectives of this module: understand the equality property of addition and multiplication, be able to solve equations of the form ax = b and x/a = b.
Overview
- Equality Property of Division and Multiplication
- Solving
and
for
Equality property of division and multiplication
Recalling that the equal sign of an equation indicates that the number represented by the expression on the left side is the same as the number represented by the expression on the right side suggests the equality property of division and multiplication, which states:
- We can obtain an equivalent equation by
dividing both sides of the equation by the same nonzero number, that is, if
then
is equivalent to
.
- We can obtain an equivalent equation by
multiplying both sides of the equation by the same nonzero number, that is, if
then
is equivalent to
.
We can use these results to isolate
thus solving the equation for
.
Solving
for
Solving
for
Solving
And
For
Method for Solving
To solve
for
,
divide both sides of the equation by
.
To solve
for
,
multiply both sides of the equation by
.
Sample set a
Solve
for
.
Solve
for
.
Solve
for
.
Method (1) (Use of cancelling):
Method (2) (Use of reciprocals):
Solve the literal equation
for
.
Practice set a
Solve
for
.
Solve
for
.
(rounded to two decimal places)
Round the result to two decimal places.
Solve
for
.
Solve
for
.
Solve
for
.
Exercises
In the following problems, solve each of the conditional equations.
Solve
for
.
Solve
for
.
Solve
for
.
Solve
for
.
Solve
for
.
Solve
for
.
Solve
for
.
Solve
for
.
Exercises for review
(
[link] ) Simplify
.
(
[link] ) Classify
as a monomial, binomial, or trinomial. State its degree and write the numerical coefficient of each item.
binomial; 3rd degree;
(
[link] ) Simplify
.
(
[link] ) Specify the domain of the equation
.
all real numbers except
(
[link] ) Solve the conditional equation
.